The Stars were trailing 1-0 when Seguin struck for the first of his goals 39 seconds into the period for the equalizer. He added back-to-back scores 22 seconds apart later in the period for his third career hat trick.
Valeri Nichushkin assisted on all three of Seguin's goals and added a score of his own for Dallas, which was coming off a 3-2 overtime loss to Toronto Thursday.
Cody Eakin supplied a short-handed goal and Dan Ellis stopped 27-of-28 shots.
Andrej Meszaros scored for the Flyers.
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